DUALITY OF TIME:

Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef

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2.20  Electromagnetism

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Static electricity and magnetism were known from ancient times, but the serious study of electricity began after the electrostatic generator was invented by Otto von Guerike (1602-1686 AD), and even more after the continuous voltaic cell by Alessandro Volta (1745-1827 AD) in Italy in 1799. Benjamin Franklin (1705-1790 AD) suggested that there are positive and negative charges, with like charges repelling each other and unlike charges attracting, and he showed that there was a connection between electricity and magnetism.

In 1750 John Mitchell (1724-1793 AD) discovered the inverse-square repulsion of magnetic poles, and after several decades Charles Coulomb (1736-1806 AD) showed that both the magnetic and electric forces experienced an inverse-square dependence on distance. In electrostatics, this is now called Coulomb’s law:

(2.5)

Andre Ampere (1775-1836 AD) developed a theory for the calculating the magnetic forces caused by a given electrical current, then Michael Faraday (1791-1867 AD) developed many experiments which led to the generation of electricity by mechanical means. Faraday also suggested that the forces of electricity or magnetism acted through lines that later were called “field”, which proved to be one of the most powerful of all theoretical tools of modern physics, because the concept will be generalized later in many ways in Relativity and Quantum Field Theory as we shall discuss in chapter III.

Maxwell later was able to describe these lines of force using Newtonian mechanics, envisioning them as rotating tubes of fluid (the aether) which had the properties required by Faraday: the rotation would cause the tubes to expand laterally and contract longitudinally. The resulting set of only four equations, Maxwell’s equations, described all known electric and magnetic phenomena exactly.

Maxwell’s equations describe how electric charges and electric currents create electric and magnetic fields. They also describe how an electric field can generate a magnetic field, and vice versa.

1.The first equation allows you to calculate the electric field created by a charge:(2.6) 2.The second allows you to calculate the magnetic field(2.7) 3.The other two describe how fields ’circulate’ around their sources, Magnetic fields ’circulate’ around electric currents and time varying electric fields, Ampere’s law with Maxwell’s correction(2.8) 4.while electric fields ’circulate’ around time varying magnetic fields, Faraday’s law(2.9)

whereis the divergence operator,is the curl operator,is the electric field in units of volt per meter,is the magnetic field strength in ampere per meter,is the electric displacement field in coulomb per square meter,is the magnetic flux density in tesla,is the free electric charge density in coulomb per cubic meter, andis the free current density in ampere per square meter.

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